zic {zic}R Documentation

Bayesian Inference for Zero-Inflated Count Models

Description

zic fits zero-inflated count models via Markov chain Monte Carlo methods.

Usage

zic(formula, data, bbar, dbar, ebar, fbar, n.burnin, n.mcmc, n.thin)

Arguments

formula A symbolic description of the model to be fit specifying the response variable and covariates.
data A data frame in which to interpret the variables in formula.
bbar The diagonal elements of the prior variance matrix of beta, a vector of length equal to the number of covariates.
dbar The diagonal elements of the prior variance matrix of delta, a vector of length equal to the number of covariates.
ebar The shape parameter for the inverse gamma prior on sigma^2.
fbar The inverse scale parameter the inverse gamma prior on sigma^2.
n.burnin Number of burn-in iterations of the sampler.
n.mcmc Number of iterations of the sampler.
n.thin Thinning interval.

Details

The considered zero-inflated count model is given by

y*_i ~ Poisson[exp(eta*_i)],

eta*_i = x_i' * beta + epsilon_i, epsilon_i ~ N( 0, sigma^2 ),

d*_i = x_i' * delta + nu_i, nu_i ~ N( 0, 1 ),

y_i = 1(d*_i>0) y*_i,

where y_i and x_i are observed. The assumed prior distributions are

beta ~ N(0,Bbar) with Bbar = diag(bbar1,...,bbark),

delta ~ N(0,Dbar) with Dbar = diag(dbar1,...,dbark),

sigma^2 ~ Inv-Gamma(ebar,fbar).

The sampling algorithm developed by Jochmann (2009) is used.

Value

A list containing the following elements:

beta The posterior draws for beta.
delta The posterior draws for delta.
sigma2 The posterior draws for sigma^2.

References

Jochmann, M. (2009). ``What Belongs Where? Variable Selection for Zero-Inflated Count Models with an Application to the Demand for Health Care''. Available at: http://personal.strath.ac.uk/markus.jochmann.

Examples

# library( zic )
# data( docvisits )

# prior parameters and formula
# bbar <- rep( 10.0, 16 )
# dbar <- rep( 10.0, 16 )
# ebar <- 3.0
# fbar <- 2.0
# formula <- docvisits ~ age + agesq + health + handicap + hdegree +
#            married + schooling + hhincome + children + self +
#            civil + bluec + employed + public + addon 

# set seed and run MCMC sampler
# set.seed(1)
# results <- zic( formula, docvisits, bbar, dbar, ebar, fbar, 10000, 100000, 10 )

# print posterior means for beta
# apply( results$beta, 2, mean )

[Package zic version 0.5-3 Index]